This study presents 1.) a multi-dimensional model of vanadium Redox Flow Batteries (RFB); 2.) rigorous explanation of pore-level transport resistance, dilute solution assumption, and pumping power; and 3.) analysis of time constants of heat and mass transfer and dimensionless parameter. The model, describing the dynamic system of a RFB, consists of a set of partial differential equations of mass, momentum, species, charges, and energy conservation, in conjunction with the electrode's electrochemical reaction kinetics. The governing equations are successfully implemented into three-dimensional numerical simulation of charging, idling, and discharging operations. The model, validated against experimental data, predicts fluid flow, concentration increase/decrease, temperature contours and local reaction rate. The prediction indicates a large variation in local reaction rate across electrodes and the time constants for reactant variation and temperature evolution, which are consistent with theoretical analysis. (C) 2014 The Electrochemical Society. All rights reserved.